Tree, shurb, weed?

So I have two unidentified new plants growing pretty fast. They both look like they could be trees. They popped up around 4-6 months ago. They are growing where I don't normally cut the grass and I'm wondering what they actually are and if they are worth keeping around.

If I keep them, I would want to replant them in a suitable place. One is growing kind of under the kids trampoline in the backyard. The other is growing on the side of the house, right next to the brick wall. The leaves for both are diffrent and look like no other tree around me.

Here's the first one. This grew last spring, but died after a month or two. Around April I think, I noticed something growing again. This is how big it is now.
Close up of the leaf

Here is the one in the backyard. This one sprung up about the same time. Close up of the trunk.
Close up of the leaf

If it grows that fast, it isn't a tree. If it is difficult to pull from the ground it is a weed. We have these things growing on our property, and they take over things. I am not sure what they are called, but you can wait on others to respond with a name.